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According to Newton’s second law of motion, the rate of change of the momentum of an object is the net external force acting on it. The total change in momentum between two timepoints thus depends on both the external force acting on it and the time over which it acts. Describing this mathematically, the total change of an object’s motion is proportional to the force vector and the time over which it is applied. This product is called impulse.
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Related Experiment Video

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In Vivo Measurement of Hindlimb Dorsiflexor Isometric Torque from Pig
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Force-Time Entropy of Isometric Impulse.

Tsung-Yu Hsieh1, Karl M Newell2

  • 1a Department of Kinesiology , Pennsylvania State University , University Park.

Journal of Motor Behavior
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Force and timing variability in discrete movements are linked. Joint force-time entropy analysis reveals this relationship, with optimal performance occurring in a middle range of force and timing parameters.

Keywords:
force-time constraintsimpulse variabilityinformation entropyisometric force task

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Area of Science:

  • Motor Control
  • Biomechanics
  • Human Movement Science

Background:

  • Previous research debated whether force and temporal variability in discrete impulse production are independent or dependent on force rate.
  • Understanding the interplay between force characteristics and timing variability is crucial for explaining motor control strategies.

Purpose of the Study:

  • To investigate the joint relationship between force and temporal variability in isometric single finger force production.
  • To examine how force level and time to peak force influence force and timing error variability and entropy.

Main Methods:

  • Two experiments were conducted using an isometric single finger force task.
  • Experiment (a) manipulated force level while keeping time to peak force constant.
  • Experiment (b) manipulated time to peak force while keeping the force level constant.
  • Joint force-time entropy was analyzed to quantify the relationship between force and temporal variability.

Main Results:

  • Peak force variability increased with higher force levels and shorter times to peak force.
  • Shorter times to peak force also led to reduced timing error variability.
  • Peak force entropy and time to peak force entropy increased as conditions approached maximum force or minimum force production rate.
  • Joint force-time entropy was minimized in the middle parameter range of discrete impulse.

Conclusions:

  • Force error and timing error are dependent and complementary within a joint force-time entropy framework.
  • Motor control strategies aim to minimize joint force-time entropy, suggesting an optimal range for force and timing parameters.
  • The findings challenge independent views and support a dependent relationship, modulated by force rate and level.